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Calculus and Optimization for Machine Learning
Week 1
Practice Quiz #2

Practice QuizPractice Quiz • 15 min15 minutes

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Practice Quiz #2

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Practice Quiz #2

Total points 4

1.

Question 1

Compute the limit:

lim n \to \infty n 3 - n 2 + 4 + 2 n 4 0.1 n 3 + n 5 - 1335

1 / 1 point

0

0

Correct

Correct!

2.

Question 2

Compute the limit:

lim n \to \infty ln (1 + sin 1 n) cos 2 π n!

1 / 1 point

0

0

Correct

Correct!

3.

Question 3

Without any additional transformations, define the type of the indeterminate form (consider the form of the whole expression, not its parts) in the limit of:

a n = (1 + 2 n 2 4 n 2 - 4 n) n

1 / 1 point

$1^\infty$

$\infty^\infty$

$(1/2)^\infty$

not the indeterminate form

Correct

4.

Question 4

Without any additional transformations, define the type of the indeterminate form (consider the form of the whole expression, not its parts) in the limit of:

a n = n 2 \cdot ln cos 1 n

1 / 1 point

not the indeterminate form

$0\cdot \infty$

$\infty \cdot 1$

$\infty \cdot \infty$

Correct

Correct!

ˆ